The present invention relates generally to cell coloring techniques for telecommunications service coverage areas. More specifically, but without limitation thereto, the present invention relates to minimizing the number of cell colors required in coverage areas serviced by high altitude transponder platforms for fixed and mobile communications.
Transponder platforms for CDMA communications typically use spot beams to isolate cells assigned the same color, i.e., those using the same allocation of system resources such as CDMA codes, frequency, time slot, etc. Each color, or subset of available resources, corresponds to a specific allocation of system resources, and the coloring pattern is done in such a way as to ensure minimal interference between signals transmitted to or received from adjacent cells by allowing only differently colored cells to share a common border.
A primary figure of merit for conventional cell coloring techniques is the minimum distance between cells assigned the same color. Individual cells are typically defined by spot beams formed by an antenna, and the response of such beams does not generally roll off sharply at the edges. The isolation between cells assigned the same color may be increased by increasing their spatial separation, but this approach sacrifices utilization of total resources allocated to communications, or equivalently, increases the number of colors. Two common cell coloring schemes for cells defined by individual spot beams are the four color scheme and the seven color scheme.
FIG. 1 is a diagram illustrating a standard four color scheme 100 of the prior art. Each color is illustrated by a different shading pattern and represents a unique assignment of resources, for example, one or more CDMA codes, time slots, and/or frequency bands. Each cell 102 is typically illuminated by a single spot beam from a transponder platform. In this example, each cluster 104 of four colors has the shape of a rhombus that contains exactly one hexagonal cell 102 of each color centered on each vertex respectively of the rhombus. The cells 102 and the clusters 104 are arranged as shown on a rhombic grid to cover an area of arbitrary size such that any two cells assigned the same color are separated by at least one cell assigned a different color.
FIG. 2 is a diagram illustrating a standard seven color scheme 200 of the prior art. In this example, each cluster 202 has the shape of a hexagon and contains exactly one hexagonal cell 204 of each color centered on each vertex respectively of the hexagon, with the seventh cell being centered at the geometric center of the hexagon. The cells 204 and the clusters 202 are arranged as shown on a hexagonal grid to cover an area of arbitrary size such that any two cells assigned the same color are separated by at least two cells assigned different colors.